Excellence in Research and Innovation for Humanity

Changqing Yang

Publications

3

Publications

3
16752
Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method
Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords:
Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.
2
7461
Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method
Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords:
Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.
1
16762
Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind
Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords:
Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.